Chapter 2: Q320. (page 184)

Solve the inequality, graph the solution on the number line and write the solution in the interval notation.
$8 m - 2 (14 - m) \geq 7 (m - 4) + 3 m$

Short Answer

Expert verified

Identity

$(- \infty, \infty)$

Step by step solution

Step 1. Given information

The following inequality is given

$8 m - 2 (14 - m) \geq 7 (m - 4) + 3 m$

Step 2. Solving the inequality.

Distributing and combining like terms

$8 m - 28 + 2 m \geq 7 m - 28 + 3 m 10 m - 28 \geq 10 m - 28$

Subtracting $10 m$ from both sides

$10 m - 28 - 10 m \geq 10 m - 28 - 10 m - 28 \geq - 28$

Since no variables are present and we have a true statement, inequality is an identity. The solution will be all real numbers.

Step 3. Graphing the solution on the number line

The graph of the solution on the number line is presented below:

Step 4. Writing the solution in the interval notation.

The solution, in the interval notation, can be written as

$(- \infty, \infty)$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Solve the inequality, graph the solution on the number line and write the solution in the interval notation.
$8 m - 2 (14 - m) \geq 7 (m - 4) + 3 m$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solving the inequality.

Step 3. Graphing the solution on the number line

Step 4. Writing the solution in the interval notation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Calculus

Pure Maths

Discrete Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Solve the inequality, graph the solution on the number line and write the solution in the interval notation.8m-214-m≥7m-4+3m

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solving the inequality.

Step 3. Graphing the solution on the number line

Step 4. Writing the solution in the interval notation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Calculus

Pure Maths

Discrete Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Solve the inequality, graph the solution on the number line and write the solution in the interval notation.
$8 m - 2 (14 - m) \geq 7 (m - 4) + 3 m$